LOS ANGELES  Los Angeles Police Chief Charlie Beck recapped the Christopher Dorner investigation Tuesday, saying he wants the $1 million reward to be paid out, and that a review of the ex-officer’s firing will likely take months.

Beck said there were 31 private and municipal donors to the fund offering a reward for Dorner’s arrest and conviction.

Several people are claiming to deserve the money, saying it was their tip that led law officers to a Feb. 12 confrontation with Dorner near Big Bear that ended in his death of a single gunshot wound believed self-inflicted.

“It had it’s desired effect, it should be paid out,” Beck said in a media conference in Los Angeles.

He said the city and county governments that contributed money have different rules on paying out rewards, and an agreement has to be reached to decide how to pay, and to whom.

Dorner, 33, was fired from LAPD in 2008 for lying in an investigation of another officer alleged to have kicked a mentally disabled man. Dorner issued an online manifesto weeks ago, declaring war on LAPD and blasting the agency for racism in a so-called effort to clear his name.

He is suspected in four subsequent murders, of a retired LAPD captain’s daughter and her fiance, a Riverside police officer and a San Bernardino County sheriff’s deputy.

Dorner’s complaints about LAPD have resonated with some, who support his contentions but not his murderous rampage.

“I don’t for a minute discard the effect Dorner’s manifesto has had on the reputation of the Los Angeles Police Department,” Beck said Tuesday.

He said he wants to address the allegations of agency racism and make the results public. Beck said a report on the findings will go first to the Inspector General, then the department’s police commission, a process that will likely take months.

If investigators decide to reopen the entire case leading up to Dorner being fired, the probe could take even longer, Beck said.